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Edgeworth expansions for centered random walks on covering graphs of polynomial volume growth

Probability 2023-06-05 v2

Abstract

Edgeworth expansions for random walks on covering graphs with groups of polynomial volume growths are obtained under a few natural assumptions. The coefficients appearing in this expansion depends on not only geometric features of the underlying graphs but also the modified harmonic embedding of the graph into a certain nilpotent Lie group. Moreover, we apply the rate of convergence in Trotter's approximation theorem to establish the Berry-Esseen type bound for the random walks.

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Cite

@article{arxiv.2011.13783,
  title  = {Edgeworth expansions for centered random walks on covering graphs of polynomial volume growth},
  author = {Ryuya Namba},
  journal= {arXiv preprint arXiv:2011.13783},
  year   = {2023}
}

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37 pages